Development and testing of stable, invariant, isoparametric curvilinear 2- and 3-D hybrid-stress elements. (English) Zbl 0535.73057

Linear and quadratic Serendipity hybrid-stress elements are examined in respect of stability, coordinate invariance, and optimality. A formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements. The resulting least-order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles. A distortion sensitivity study for two- and three-dimensional elements provides favourable numerical comparisons with the assumed displacement method.


74S05 Finite element methods applied to problems in solid mechanics
74S99 Numerical and other methods in solid mechanics
Full Text: DOI


[1] Pian, T.H.H.; Tong, P., Finite element methods in continuum mechanics, () · Zbl 0149.42802
[2] Atluri, S.N., On ‘hybrid’ finite element models in solid mechanics, (), 346-356, University of Ghent (Belgium)
[3] Atluri, S.N.; Tong, P.; Murakawa, H., Recent studies in hybrid and mixed finite element methods in mechanics, () · Zbl 0407.73038
[4] Pian, T.H.H.; Da-Peng, Chen; Kang, D., A new formulation of hybrid/mixed finite element, Comput. & structures, 16, 1-4, 81-87, (1983) · Zbl 0498.73073
[5] Bicanic, N.; Hinton, E., Spurious modes in two-dimensional isoparametric elements, Internat. J. numer. meths. engrg., 14, 1545-1557, (1979) · Zbl 0411.73064
[6] Brezzi, F., On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, Rairo 8-r2, 129-151, (1974) · Zbl 0338.90047
[7] Babuska, I.; Oden, J.T.; Lee, J.K.; Babuska, I.; Oden, J.T.; Lee, J.K., Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems, part I, Comput. meths. appl. mech. engrg., Weak hybrid methods, 14, 1-22, (1978) · Zbl 0401.65068
[8] Spilker, R.L.; Maskeri, S.M.; Kania, E., Plane isoparametric hybrid-stress elements: invariance and optimal sampling, Internat. J. numer. meths. engrg., 17, 1469-1496, (1981) · Zbl 0462.73050
[9] Yang, C-T.; Rubinstein, R.; Atluri, S.N., On some fundamental studies into the stability of hybrid-mixed finite element methods for Navier/Stokes equations in solid/fluid mechanics, (), 24-76, (1982), Georgia Tech.
[10] Rubinstein, R.; Punch, E.F.; Atluri, S.N., An analysis of, and remedies for, kinematic modes in hybrid-stress finite elements: selection of stable, invariant stress fields, Comput. meths. appl. mech. engrg., 38, 63-92, (1983) · Zbl 0519.73070
[11] E.F. Punch and S.N. Atluri, Applications of isoparametric three-dimensional hybrid-stress finite elements with least-order stress fields, Comput. & Structures (in press). · Zbl 0552.73062
[12] Henshell, R.D., On hybrid finite elements, () · Zbl 0281.73048
[13] Atluri, S.N.; Murakawa, H.; Bratianu, C., Use of stress functions and asymptotic solutions in FEM analysis of continua, (), 11-28 · Zbl 0464.73099
[14] Tong, P.; Pian, T.H.H., A variational principle and convergence of a finite element method based on assumed stress distributions, Internat. J. solids structures, 5, 463-472, (1969) · Zbl 0167.52805
[15] Hamermesh, M., Group theory and its application to physical problems, (1962), Addison-Wesley Reading, MA · Zbl 0151.34101
[16] Punch, E., Stable, invariant, least-order isoparametric mixed-hybrid stress elements: linear elastic continua, and finitely deformed plates and shells, ()
[17] Wilson, E.L.; Taylor, R.L.; Doherty, W.P.; Ghabussi, T., Incompatible displacement models, ()
[18] Cook, R.D., An improved two-dimensional finite element, ASCE J. struct. div., 9, (1974)
[19] Pian, T.H.H.; Sumihara, K.; Kang, D., New variational formulations of hybrid stress elements, (1983), NASA Lewis Research Center, presented at
[20] Taylor, R.L.; Beresford, P.J.; Wilson, E.L., A non-conforming element for stress analysis, Internat. J. numer. meths. engrg., 10, (1976) · Zbl 0338.73041
[21] T.H.H. Pian and D.P. Chen, On the suppression of zero energy deformation modes, Internat. J. Numer. Meths. Engrg. (to appear). · Zbl 0537.73059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.